ALBERT

Description: In this paper, the (2+1)-dimensional Saweda-Kotera-Kadomtsev-Petviashvili (SK-KP) equation is investigated, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. With the aid of generalized Bell’s polynomials, the Hirota’s bilinear equation and N -soliton solution are explicitly constructed to the SK-KP equation, respectively. Based on the Riemann theta function, a direct and lucid way is presented to explicitly construct quasi-periodic wave solutions for the SK-KP equation. The two-periodic waves admit two independent spatial periods in two independent horizontal directions, which are a direct generalization of one-periodic waves. Finally, the relationships between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure.

Description: . This work is a continuation of the previous series related to the construction of the energy matrix for complex atoms. The effects of the second-order configuration interaction perturbations on the energy-level structure of \(nl^{N}\) , \( nl^{N}n_{1}l_{1}^{N_{1}}\) and \( nl^{N}n_{1}l_{1}^{N_{1}}n_{2}l_{2}\) configurations were studied. In this paper we consider one-electron core excitations for and between the configurations under study. This work combined with Part II and III is a complete description of an electrostatic interaction. In Part I we presented a method which allows to analyse complex electronic systems. They constitute the basis for the design of an efficient computer program package allowing large scale calculations which provide accurate wave functions.

Description: Following the recent establishment of an exact kinetic theory realized by the Master kinetic equation which describes the statistical behavior of the Boltzmann-Sinai Classical Dynamical System (CDS), in this paper the problem is posed of the construction of the related global existence and regularity theorems. For this purpose, based on the global prescription of the same CDS for arbitrary single- and multiple-collision events, first global existence is extablished for the N -body Liouville equation which is written in Lagrangian differential and integral forms. This permits to reach the proof of global existence both of generic N -body probability density functions (PDF) as well as of particular solutions which maximize the statistical Boltzmann-Shannon entropy and are factorized in terms of the corresponding 1-body PDF. The latter PDF is shown to be uniquely defined and to satisfy the Master kinetic equation globally in the extended 1-body phase space. Implications concerning the global validity of the asymptotic Boltzmann equation and Boltzmann H-theorem are discussed.

Description: We show that single-slit two-photon ghost diffraction can be explained very simply by using a wave-packet evolution of a generalised EPR state. Diffraction of a wave travelling in the x -direction can be described in terms of the spreading in time of the transverse ( z -direction) wave-packet, within the Fresnel approximation. The slit is assumed to truncate the transverse part of the wave function of the photon to within the width of the slit. The analysis reproduces all features of the two-photon single-slit ghost diffraction.

Description: In this paper, the combined effects of Hall current and magnetic field on the onset of convection in an electrically conducting nanofluid layer heated from below is investigated. A physically more realistic boundary condition on the nanoparticle volume fraction is taken i.e. the nanoparticle flux is assumed to be zero rather than prescribing a nanoparticle volume fraction on the rigid impermeable boundaries. The employed model incorporates the effects of Brownian motion and thermophoresis. The resulting eigenvalue problem is solved using the Galerkin method. The results obtained during the analysis are presented graphically for an alumina-water nanofluid. It is observed that the effect of smaller values of the Hall current parameter and the nanoparticle parameters accelerate the onset of convection, while larger values of the Hall current parameter (≥ 15) have no effect on the system stabilities.

Description: The rotary oscillation of a composite sphere, consisting of a solid core surrounded by a porous shell, in an incompressible viscous fluid bounded by a concentric spherical cavity is investigated using the Brinkman model. The stress jump condition is applied on the porous-fluid interface and the slip boundary condition is proposed on the surface of the spherical cavity. The couple exerted by the fluid on the porous surface is obtained analytically and its imaginary and real coefficients are represented graphically. The effects of slip parameter, permeability coefficient, stress jump coefficient and effective viscosity ratio on the torque are discussed and special cases are deduced.

Description: In this paper I consider surfaces in a space-time with a Killing vector ξ α that is time-like and hypersurface-orthogonal on one side of the surface. The Killing vector may be either time-like or space-like on the other side of the surface. It has been argued that the surface is null if ξ α ξ α → 0 as the surface is approached from the static region. This implies that, in a coordinate system adapted to ξ , surfaces with g tt = 0 are null. In spherically symmetric space-times the condition g rr = 0 instead of g tt = 0 is sometimes used to locate null surfaces. In this paper I examine the arguments that lead to these two different criteria and show that both arguments are incorrect. A surface ξ = const has a normal vector whose norm is proportional to ξ α ξ α . This lead to the conclusion that surfaces with ξ α ξ α = 0 are null. However, the proportionality factor generally diverges when g tt = 0, leading to a different condition for the norm to be null. In static spherically symmetric space-times this condition gives g rr = 0, not g tt = 0. The problem with the condition g rr = 0 is that the coordinate system is singular on the surface. One can either use a nonsingular coordinate system or examine the induced metric on the surface to determine if it is null. By using these approaches it is shown that the correct criteria is g tt = 0. I also examine the condition required for the surface to be nonsingular.

Description: Alba is a 3rd-generation 3 GeV synchrotron facility with an emittance of 4.6nm·rad which has been operational since 2011 and has recently started top-up operation. Photons in a broad energy range of 0.08-80 keV are served to seven beamlines dedicated to a large variety of scientific fields. The portfolio includes two beamlines, XALOC and MSPD, fully dedicated to X-ray crystallography. BL13-XALOC is currently the only macromolecular crystallography beamline. The end-station includes a high-accuracy single-axis diffractometer with a removable minikappa stage, a sample-mounting robot and a large-area, photon-counting detector. The beamline optics, fed by an in-vacuum undulator, deliver a tunable photon beam between 5.5 and 22 keV. The beam size at the sample position can be adjusted by defocusing the mirrors in a range of 50-300μm in the horizontal direction and 5.5-300μm in the vertical direction. Beamline BL04-MSPD, which is fed by a superconducting wiggler, has two in-line end-stations. The first station is devoted to high-pressure/microdiffraction. It offers a \( 15\times 15\) μm beam in the range 20-50 keV, particularly suited for powder diffraction studies requiring a very small beam, e.g. mapping of cultural heritage samples and high-pressures studies. The second station is dedicated to high-resolution/high-throughput powder diffraction. It covers the 8-50 keV range and includes a heavy-duty 3-circle diffractometer equipped with a 13-channel multianalyzer detector with high-angular resolution ( \( \Delta 2\theta=0.004^{\circ}\) FWHM) and a high-throughput, position-sensitive detector spanning \( 40^{\circ}\) in 2 \( \theta\) range allowing millisecond data acquisitions.

Description: In this research, an AlGaAs film was deposited on a microscope slide by means of the thermionic vacuum arc (TVA) technique which is a novel plasma production technique. AlGaAs structures were grown by this deposition technique for the first time and this process occurred in a very short period of time. In order to characterize the produced film, nano-structural, nano-mechanical, optical, and surface properties were determined by field emission scanning electron microscope (FESEM), atomic force microscope (AFM), X-ray diffractometer (XRD) and interferometer. According to the results of the measurements, the mean thickness value of the produced film was obtained as 1.8 μ m. The band gap value was determined as 2eV from the Kubelka-Munk plot. The refractive index value was obtained as approximately 3.4. Hardness value was determined as 2 GPa from the Oliver-Pharr method. All these values are consistent with the reported values in the literature for the AlGaAs films produced by different methods. TVA technique appeared as a suitable and promising technique for the production of AlGaAs films.

Description: This paper deals with a numerical study of natural convection flow and heat transfer inside a concentric horizontal annulus filled with a porous medium saturated by a cuprum (Cu)-water nanofluid. The inner and outer cylinders are kept at different constant temperatures. First, the governing partial differential equations in dimensional formulation in a polar coordinate system for the physical domain are transformed in dimensionless form in terms of stream function-temperature formulation. These equations along with the corresponding boundary conditions were solved numerically by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, porosity of the porous medium, solid volume fraction parameter of nanoparticles, annulus radius ratio, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It is found that a very good agreement exists between the present results and those from the open literature.